J Neurophysiol 95: 3617–3632, 2006.
First published February 22, 2006; doi:10.1152/jn.00004.2006.
Central Pattern Generating Neurons Simultaneously Express Fast and Slow
Rhythmic Activities in the Stomatogastric Ganglion
Dirk Bucher, Adam L. Taylor, and Eve Marder
Volen Center and Biology Department, Brandeis University, Waltham, Massachusetts
Submitted 3 January 2006; accepted in final form 21 February 2006
INTRODUCTION
Neurons and networks can produce activity that simultaneously carries information about different processes. This is
achieved either by coding different information in different
frequency bands or by using different coding modalities at
different time scales. For example, network oscillations in the
mammalian forebrain at different frequency bands can either
be associated with different brain states, or coexist and interact
(Buzsaki and Chrobak 1995; Buzsaki and Draguhn 2004;
Steriade 2005). In the zebrafish olfactory bulb, seemingly
alternative coding strategies, namely rate coding and spike
synchrony, potentially coexist (Friedrich et al. 2004). Electrosensory pyramidal cells in weakly electric fish produce spike
trains in response to broadband input that consist of two
parallel information streams, one using bursts and one using
single spikes (Oswald et al. 2004).
Examples of simultaneous expression of more than one
pattern are also found in neuronal and network activity that
Present address and address for reprint requests and other correspondence:
D. Bucher, Whitney Laboratory and Department of Neuroscience, University
of Florida, 9505 Ocean Shore Blvd., St. Augustine, FL 32080 (E-mail:
[email protected]).
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produces different rhythmic motor output at different cycle
periods. Interactions between either motor patterns can be due
to sensory feedback that reports movement of one part of the
body and affects pattern generation for another part or to
central connections between central pattern generating (CPG)
circuits (Marder et al. 2005). For example, the respiratory CPG
in the rat can be reset and entrained at integer multiples of the
period of rhythmic sensory feedback reporting leg movements.
This is thought to provide coordination between locomotion
and breathing (Morin and Viala 2002; Potts et al. 2005).
In contrast, interactions between networks in the stomatogastric nervous system (STNS) are present even in the absence
of sensory feedback. The STNS controls rhythmic movements
in different parts of the stomach in decapod crustaceans (Harris-Warrick et al. 1992; Selverston and Moulins 1987). The
stomatogastric ganglion (STG) contains two networks, one
controlling the teeth of the gastric mill and one controlling the
pyloric filter apparatus. These networks are composed of neurons that act both as part of their respective CPGs and as motor
neurons that send axons to specific stomach muscles. The
gastric pattern has a cycle period on the order of 5–20 s,
whereas the pyloric pattern has a cycle period on the order of
1–2 s.
STG neurons, as well as other neurons in the STNS, can
switch from one pattern to another, and modulatory input can
reconfigure circuits to produce different types of coordination
between neurons controlling separate parts of the stomach
(Dickinson 1995; Dickinson et al. 1990; Hooper and Moulins
1989, 1990; Marder et al. 2005; Meyrand et al. 1991, 1994;
Weimann and Marder 1994). Many of these neurons also
express rhythmic activity of multiple patterns at the same time,
reflecting influences of two or more networks. Gastric neurons
can show clear pyloric modulation of their firing pattern during
the phase in the gastric cycle in which they are active, and
pyloric neurons can show modulation of their bursting activity
over the course of a gastric cycle (Heinzel 1988a; Heinzel and
Selverston 1988; Mulloney 1977; Thuma and Hooper 2002;
Weimann et al. 1991). These interactions are mediated by
direct chemical and electrical synapses between members of
the pyloric and gastric networks (Bartos et al. 1999; Clemens
et al. 1998; Mulloney 1977; Selverston et al. 1976) and by
coordinating influences from descending neurons (Bartos and
Nusbaum 1997; Wood et al. 2004).
Coordinated activity among two or more CPGs is important
for behavior involving multiple body parts. However, the
presence of interactions between two CPGs does not automatThe costs of publication of this article were defrayed in part by the payment
of page charges. The article must therefore be hereby marked “advertisement”
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
0022-3077/06 $8.00 Copyright © 2006 The American Physiological Society
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Bucher, Dirk, Adam L. Taylor, and Eve Marder. Central pattern generating neurons simultaneously express fast and slow
rhythmic activities in the stomatogastric ganglion. J Neurophysiol
95: 3617–3632, 2006. First published February 22, 2006;
doi:10.1152/jn.00004.2006. Neuronal firing patterns can contain
different temporal information. It has long been known that the fast
pyloric and the slower gastric motor patterns in the stomatogastric
ganglion of decapod crustaceans interact. However, the bidirectional influences between the pyloric rhythm and the gastric mill
rhythm have not been quantified in detail from preparations that
spontaneously express both patterns in vitro. We found regular and
stable spontaneous gastric and pyloric activity in 71% of preparations of the isolated stomatogastric nervous system of the lobster,
Homarus americanus. The gastric [cycle period: 10.96 ⫾ 2.67
(SD) s] and pyloric (cycle period: 1.35 ⫾ 0.18 s) patterns showed
bidirectional interactions and coordination. Gastric neuron firing
showed preferred phases within the reference frame of the pyloric
cycle. The relative timing and burst parameters of the pyloric
neurons systematically changed within the reference frame of the
gastric cycle. The gastric rhythm showed a tendency to run at cycle
periods that were integer multiples of the pyloric periods, but
coupling and coordination between the two rhythms were variable.
We used power spectra to quantify the gastric and pyloric contributions to the firing pattern of each individual neuron. This
provided us with a way to analyze the firing pattern of each gastric
and pyloric neuron type individually without reference to either
gastric or pyloric phase. Possible functional consequences of these
network interactions for motor output are discussed.
3618
D. BUCHER, A. L. TAYLOR, AND E. MARDER
METHODS
Adult lobsters, H. americanus (weight: ⬃500 g), were purchased
from Yankee Lobster (Boston, MA). Animals were kept at 10 –13°C
in recirculating artificial seawater tanks. All animals were coldanesthetized prior to dissection. Dissections were carried out in saline
containing (in mM) 479.12 NaCl, 12.74 KCl, 13.67 CaCl2, 20
Mg2SO4, 3.91 Na2SO4, and 5 HEPES, pH ⫽ 7.4 –7.5. The STNS was
dissected and pinned out in transparent silicone elastomer (Sylgard)coated (Dow Corning, Midland, MI) dishes containing chilled (9 –
13°C) saline. The paired commissural ganglia (CoGs), the esophageal
ganglion (OG), the STG, their connecting nerves, and many of the
peripheral motor nerves were kept intact. The STG was always
desheathed.
Electrophysiological recordings
Maynard and Dando (1974) described the innervation of the stomach muscles in H. americanus using slightly different terminology
than the one Mulloney and Selverston (1974) established for the spiny
lobster, P. interruptus. Because the latter has prevailed in a number of
different species, including the closely related Homarus gammarus (e.g.,
Robertson and Moulins 1984), we also adopted it for H. americanus.
Figure 1 schematically depicts the innervation pattern of the stomach muscles (Claiborne and Ayers 1987; Maynard and Dando 1974).
The lateral gastric (LG) neuron, the dorsal gastric (DG) neuron, the
medial gastric (MG) neuron, the gastric mill (GM) neurons, and the
lateral posterior gastric (LPG) neurons innervate muscles that move
the teeth of the gastric mill. The LPG neurons also innervate pyloric
muscles. The GM neurons are responsible for the power stroke of the
medial tooth, whereas the LG and MG neurons control the power
stroke of the lateral teeth. The DG neuron controls the return stroke of
the medial tooth, and the LPG neurons the return stroke of the lateral
teeth. The pyloric dilator (PD) neurons and the lateral pyloric (LP)
neuron innervate muscles that move the pylorus and the cardio-pyloric
valve. The pyloric (PY) neurons innervate muscles that move the
pylorus. The ventricular dilator (VD) neuron and the inferior cardiac
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(IC) neuron innervate muscles that move the ventral cardiac ossicles,
and thereby the cardio-pyloric valve. The anterior median (AM)
neuron innervates dorsal cardiac muscles.
Extracellular recordings were obtained by placing stainless steel
wires into small (⬃1 mm) petroleum-jelly wells around specific
nerves (Fig. 1B). Signals were amplified and filtered using differential
AC amplifiers (A-M Systems, Carlsborg, WA).
Intracellular recordings from the STG neuron somata were made
using 20 – 40 M⍀ glass microelectrodes filled with 0.6 M K2SO4 and
20 mM KCl and amplified using an Axoclamp 2B amplifier (Axon
Instruments, Foster City, CA). Cells were identified by their characteristic waveforms and correspondence of intracellular spikes with
extracellular spikes in the nerve recordings. The pyloric and gastric
networks include two interneurons, the anterior burster (AB) and
interneuron 1 (Int1). These two neurons have ascending axons in the
stomatogastric nerve, but the signal-to-noise ratio in extracellular
recordings was low, and we therefore did not include these cells in any
quantitative analyses.
Data acquisition and analysis
Recordings were digitized using a DigiData 1200 data-acquisition
board (Axon Instruments) and analyzed with Spike2 (version 5, CED,
Cambridge, UK) and MATLAB (version 7, The MathWorks, Natick,
MA) using programs written in the respective script languages. Spike
time detection was achieved either by using simple thresholding or, if
more than one signal amplitude was present in a nerve recording, by
using window discrimination. For neurons that exist in two copies (PD
and LPG), unambiguous spike detection was still possible because
summation of extracellular signals took place only occasionally and
could easily be taken into account. However, there are multiple copies
of PY and GM neurons, and in the STG of H. americanus there is
variability in their numbers from animal to animal (Bucher and
Marder, unpublished results). The extent of summation of extracellularly recorded signals made unambiguous spike detection impossible
for these two neuron types. Therefore wherever changes in number of
spikes and spike frequency are described for the PY and GM neurons
here, they represent relative rather than exact measures.
Statistical tests and plots were performed in MATLAB and Statview (version 5, SAS Institute, Cary, NC). Figures were done in
Canvas (version 10, ADC Systems, Miami, FL). Error bars represent
SD to indicate the variability of a sample and SE when statistical
comparisons were performed. Data presented here are from a total of
45 animals in which different combinations of extra- and intracellular
recordings were obtained. Unless indicated otherwise, for comparisons across different neurons only experiments were analyzed in
which recordings of all of these neurons were present. For all
statistical analyses, 10 –20 min of continuous recordings were used.
Spectral analysis
Power spectra were used to estimate how much of the variability in
a neuron’s spike rate was at pyloric/gastric frequencies. Our approach
was similar to that of Miller and Sigvardt (1998) but with a few
differences. All spectra were estimated from extracellular recordings
of a given neuron’s spike train that were 1,200 s in duration. Extracellular recordings were converted to spike times using a simple
threshold-crossing method. Spikes that occurred within 20 ms of other
spikes were deleted, to eliminate spuriously high instantaneous spike
rates (this occurs, for instance, in the PD recordings because the 2 PDs
sometimes fire nearly simultaneously). Each spike train was converted
into a spike rate, r(t), defined as one over the interspike interval of the
spikes just before and after a given time t. The “sampling rate” for r(t)
was 1 kHz. Power spectra were estimated from the r(t) signal using
multitaper spectral estimation (Percival and Walden 1993). Each
1,200-s-long signal was divided into 12 100-s-long windows, and a
spectrum was estimated for each, using a single taper. The mean of
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ically mean that there is coordination between the motor
patterns. Nadim et al. (1998) and Bartos et al. (1999) have
shown that there is integer locking between the gastric and
pyloric cycle periods in a specific version of activity elicited by
a single projection neuron, MCN1, in Cancer borealis. In
contrast, spontaneous gastric and pyloric activity in Panulirus
interruptus does not show integer locking (Thuma and Hooper
2002). In the latter case, analyzing the dynamics of one pattern
within the reference frame of the other is problematic because
averaging between cycles leads to underestimation of the
magnitude of the effects.
Here for the first time, we provide quantitative analyses of
the interactions between spontaneous pyloric and gastric activity. We do so in three different ways. First, we used the
isolated STNS of Homarus americanus to analyze gastric
neuron firing within the reference frame of the pyloric cycle.
Second, we analyzed pyloric neuron firing within the reference
frame of the gastric cycle. Third, we analyzed the firing
patterns of each neuron type individually with respect to how
much each rhythm contributes to the firing patterns. Together
these data provide a baseline quantitative description of network interactions in the H. americanus STG. Such a description will be useful for understanding how neuromodulatory
inputs might alter the extent to which networks interact and
how the discharge patterns of individual neurons reflect these
interactions.
SIMULTANEOUS FAST AND SLOW RHYTHMS IN STG NEURONS
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r(t) was subtracted off of each windowed signal prior to spectrum
estimation. The individual spectral estimates were then averaged to
yield a final spectrum estimate. The use of a single taper on a
100-s-long window resulted in a frequency resolution of 0.01 Hz. SEs
for the spectrum estimates were calculated using the jackknife estimate of variance on log-transformed spectra (Thomson and Chave
1991). We always plot the “density spectrum”, the square root of the
power density spectrum, which has units of Hz/Hz0.5 because r(t) has
units of Hz.
RESULTS
Spontaneous activity in the STNS of H. americanus
Figure 2 shows an example of simultaneous extracellular
recordings of all gastric and pyloric motor neurons. One gastric
cycle (between 2 consecutive LG neuron burst starts) is indicated by gray shading. In each gastric cycle, the LG, MG, and
GM neurons were active first, the GM neurons outlasting the
other two, followed by the LPG neurons and then the DG
neuron. The pyloric rhythm was considerably faster, as is seen
in the rhythmic activity of the PD, LP, PY, VD, IC, and AM
neurons.
Pyloric modulation of gastric neuron firing patterns and
gastric modulation of pyloric neuron firing patterns can be seen
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in some of the traces. Both the LPG neuron and the DG neuron
bursts showed clear modulation in pyloric time. The pyloric
cycle period (as defined from a PD burst start to the next), and
the IC and LP neuron burst durations were visibly larger near
the start of the gastric cycle (open arrows).
Spontaneous pyloric rhythms were found in all preparations;
gastric rhythms were found in 32 of 45 preparations (71%).
These rhythms were stable and regular over several hours of
recording time. Irregular and intermittent gastric activity was
seen in only three preparations. In preparations without a
gastric rhythm, the DG neuron and the LPG neurons continuously fired in pyloric time, whereas the LG, MG, and GM
neurons were silent.
In the past, STG neurons were sometimes subdivided into
gastric, pyloric, and gastro-pyloric neurons, based on the predominant type of activity they “normally” express (Nusbaum
and Beenhakker 2002). Alternatively, the STG has been described as a single neuron pool, the members of which can be
recruited into either one of the two rhythmic patterns dependent on neuromodulatory or sensory input (Marder and
Weimann 1992; Weimann and Marder 1994; Weimann et al.
1991, 1993, 1997). We wanted, if possible, to make a division
between gastric and pyloric neurons, simply to have a consistent terminology. For the spontaneous gastric mill rhythms that
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FIG. 1. Organization of muscles and nerves in the H. americanus stomach. A: schematic of the stomach nerves and muscles. Muscles controlling different
regions of the stomach are shown in different colors. B: schematic of the isolated stomatogastric nervous system. Typical nerve recording sites are indicated by
gray circles and labeled with the names of the neurons which have axons in these nerves. Neuron names in parentheses indicate that these axons can only
occasionally be recorded from these sites. gm, gastric muscle; p, pyloric muscle; cpv, cardio-pyloric valve muscle; cv, ventral cardiac muscle; CoG, commissural
ganglion; OG, esophageal ganglion; STG, stomatogastric ganglion; dpon, dorsal posterior esophageal nerve; son, superior esophageal nerve; stn, stomatogastric
nerve; acn, anterior cardiac nerve; avn, anterior ventricular nerve; icn, inferior cardiac nerve; agn, anterior gastric nerve; dvn, dorsal ventricular nerve; mvn,
median ventricular nerve; dgn, dorsal gastric nerve; lvn, lateral ventricular nerve; lgn, lateral gastric nerve; lpgn, lateral posterior gastric nerve; dlvn, dorsal lateral
ventricular nerve; gpn, gastro-pyloric nerve; lpn, lateral pyloric nerve; pdn, pyloric dilator nerve; pyn, pyloric nerve; AB, anterior burster; Int1, interneuron 1;
AM, anterior median neuron; IC, inferior cardiac neuron; GM, gastric mill neuron; VD, ventricular dilator neuron; LG, lateral gastric neuron; DG, dorsal gastric
neuron; LPG, lateral posterior gastric neuron; MG, medial gastric neuron; PD, pyloric dilator neuron; LP, lateral pyloric neuron; PY, pyloric neuron; The lgn
also contains the axon of the LG neuron, but it projects from lateral and is therefore distal to the cut connection between the mvn and the lgn that can be seen
in A.
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D. BUCHER, A. L. TAYLOR, AND E. MARDER
we observed, we found that it was possible to consistently label
each cell as either “gastric” or “pyloric.” We called a neuron
pyloric if it showed continuous pyloric bursting activity
throughout the entire gastric cycle. We called a neuron gastric
if it was only active in specific phases of the gastric cycle,
regardless of how much pyloric timing it expressed in its firing
pattern. We found that each identified neuron received the
same classification in all preparations that expressed both
gastric and pyloric activity.
The cells classified as pyloric by the preceding rule were the
PD, LP, PY, VD, IC, and AM neurons. The AM neuron was
either silent or firing in pyloric time. The AM neuron also fires
in pyloric time in H. gammarus (Nagy et al. 1994), whereas it
is predominantly active in gastric time in C. borealis and P.
interruptus (Selverston et al. 1976; Weimann et al. 1991). The
VD and IC neurons were never silent in part of the gastric cycle
as they can be in C. borealis (Weimann et al. 1991, 1993), and
P. interruptus (Mulloney 1977; Thuma and Hooper 2002).
The cells classified as gastric by the preceding rule include
all neurons that innervate muscles that move the teeth of the
gastric mill (LG, DG, MG, and GM neurons), and the LPG
neurons, which innervate both gastric and pyloric muscles.
preparations with both rhythms present (gastric period ⫽
10.96 ⫾ 2.67 s), the gastric cycle period and the pyloric cycle
period were not correlated (linear regression, R2 ⫽ 0.03, P ⫽
0.32, Fig. 3B).
Phase relationships of the gastric rhythm
We analyzed the gastric rhythm within the reference frame
of its own cycle. The phase relationships of the gastric neurons
have not previously been quantified in H. americanus. Because
of the complex patterns of spike timing within the bursts of
gastric neurons, we felt that plotting the phase relationships as
the commonly used bar charts would fail to represent a salient
feature of the temporal dynamics of spiking activity in the
gastric cycle, namely the changing spike rate during the burst.
In addition, for some of the neurons, strong pyloric modulation
of their firing pattern made unambiguous detection of burst
starts and burst ends difficult. We therefore divided the gastric
cycle into bins and plotted histograms of the normalized
Gastric and pyloric rhythm cycle periods
We used either the PD neuron or the VD neuron burst starts
to measure the mean pyloric cycle period in all preparations,
and, if present, the LG neuron burst starts to measure the mean
gastric cycle period. In C. borealis, the periods of gastric and
pyloric rhythms are strongly correlated when both rhythms are
elicited through stimulation of the projection neuron MCN1
(Bartos et al. 1999; Nadim et al. 1998). In H. americanus, we
found that the pyloric rhythm period was significantly longer in
preparations that did not express a gastric rhythm (1.78 ⫾
0.41 s, n ⫽ 10), than in preparations that did (1.35 ⫾ 0.18 s,
n ⫽ 32) (unpaired t-test, P ⬍ 0.0001, Fig. 3A). However, in
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FIG. 3. Gastric and pyloric cycle periods. A: pyloric rhythm period is
longer in preparations in which no gastric rhythm was present (unpaired t-test,
P ⬍ 0.0001). B: in preparations with gastric activity, the gastric and pyloric
cycle periods are not correlated (n ⫽ 32, regression analysis: R2 ⫽ 0.03, P ⫽
0.32).
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FIG. 2. Simultaneous extracellular nerve
recordings of all STG motor neurons. One
cycle of the gastric mill rhythm (between 2
LG burst starts) is indicated by gray shading.
Note the strong pyloric modulation of the
DG neuron and LPG neuron firing patterns.
Gastric effects on pyloric neuron firing pattern can also be seen: open arrows indicate
longer pyloric period (between 2 PD burst
starts) and longer IC and LP burst durations
near the start of the gastric cycle.
SIMULTANEOUS FAST AND SLOW RHYTHMS IN STG NEURONS
3621
Pyloric modulation of gastric neurons
Gastric neurons are modulated in pyloric time. This is
apparent both in the spike rates and in their membrane potential
measured with intracellular recordings. Figure 5 shows example intracellular recordings of all gastric neurons (including the
interneuron Int1, which was not part of our analysis from
extracellular recordings). In the LG, MG, and GM neurons, the
pyloric-timed modulation is particularly apparent between
strong gastric-timed bursts, whereas Int1 and the DG and LPG
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number of spikes per bin (spike density) similar to the method
used in Faumont et al. (1998).
The phase histograms shown in Fig. 4 were generated in the
following way: LG neuron burst starts were chosen as the
reference point because they were the most regular and consistent feature in the gastric cycle. For each experiment, the
time between two consecutive LG neuron burst starts was
divided into 100 bins and, for each cycle and for every neuron,
all spikes were sorted into the corresponding bin. The spike
count per bin was then divided by the total number of spikes in
that experiment and multiplied by 100, so that each bin value
represents the percentage of spikes that fell into that bin (i.e.,
every bin value would be 1 if a neuron showed no preferred
firing phase). Figure 4A shows superimposed line plots of the
histograms from 10 experiments. Three cycles are shown to
give a better sense of the repetitive pattern.
The phase relationships were generally consistent from animal
to animal. The “power stroke neurons,” LG, MG, and GM,
generally fired in the same phase. In some experiments, the
MG neuron and the GM neurons show small peaks corresponding to pyloric modulation during their burst phase as well
as small peaks outside of that phase, which correspond to
“trailing” pyloric firing (down arrows). The “return stroke
neurons”, DG and LPG, fired in anti-phase to the LG, MG, and
GM neurons but with different spike profiles during their
respective bursts. The DG neuron shows increasing spike
density during the burst, and the LPG neuron shows decreasing
spike density during the burst. In some experiments, both show
small peaks during that phase, which correspond to substantial
pyloric modulation of their firing rate (down arrows). DG neuron
activity in its specific gastric phase consisted mostly of pylorictimed bursts of increasing strength, whereas LPG neuron activity
consisted mostly of pyloric-timed bursts of decreasing strength.
Figure 4B shows histograms of the mean bin values between
experiments (shaded areas, SD). Here, each bin in each histogram represents the mean percentage of spikes that fell into
that bin. The mean phase relationships and spike dynamics
basically are the same as the ones described for the single
experiments. However, pyloric modulation of the spike patterns is less apparent. This is due to the fact that the number of
pyloric cycles per gastric cycle can differ substantially from
experiment to experiment (see following text). Therefore peaks
from pyloric influences are averaged out between experiments.
We found similar phase relationships and spike dynamics
within the bursts in all experiments analyzed. On a qualitative
level, the same was true for recordings of incomplete sets of
gastric neurons which we did not include in our analysis. Only
the LPG neurons’ onset phase was quite variable between
experiments, but no distinct types of phase relationships were
apparent.
FIG. 4. Phase relationships of gastric neurons. A: phase histograms of spike
densities from 10 different experiments. The gastric period (between consecutive LG neuron burst starts) was divided into 100 bins, and for every cycle,
spikes were sorted into corresponding bins. Bin values were then divided by
the total number of spikes. In some experiments, the MG and GM neurons
display peaks that correspond to pyloric modulation during their burst phase as
well as peaks corresponding to trailing pyloric-timed spiking between bursts
(2). The DG and LPG neurons display pyloric-timed modulation during the
peaks (2). B: phase histograms of the mean normalized spike densities from
all 10 experiments. 1, SD. Due to averaging, the pyloric-timed modulation is
less apparent than in the histograms from single experiments.
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3622
D. BUCHER, A. L. TAYLOR, AND E. MARDER
neurons show clear pyloric-timed modulation during their
gastric-timed bursts. Figure 5, right, shows multiple sweeps of
the recordings, each triggered by the extracellularly recorded
PD neuron burst starts in selected cycles. For the LG, MG, and
GM neurons, only pyloric cycles between strong gastric bursts
are shown. For the DG and LPG neurons and Int1, only pyloric
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cycles during the gastric bursts are shown. For clarity, the DG
and LPG neuron recordings were low-pass filtered to mask
spikes. We inspected the pyloric-timed membrane potential
oscillations in gastric neurons in at least five experiments per
neuron type. During their interburst interval, the LG, MG, and
GM neurons were consistently hyperpolarized during PD neu-
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FIG. 5. Pyloric modulation of gastric neuron membrane potential (mV). The LG, MG, and GM neurons show strong
pyloric-timed modulation during their interburst intervals,
whereas Int1 and the DG and LPG neurons display strong
pyloric-timed modulation during their bursts. Right: multiple
sweeps triggered from selected PD neuron burst starts to show
the membrane potential modulation in the pyloric phase. For
the LG, MG, and GM neurons, only cycles during the interburst
intervals were used. For Int1 and the DG and LPG neurons,
only cycles during the burst were used. For clarity, spikes in the
DG and LPG neurons were eliminated by low-pass filtering.
SIMULTANEOUS FAST AND SLOW RHYTHMS IN STG NEURONS
3623
of spikes and multiplied by 100 so that every bin value
represents the percentage of spikes at the corresponding pyloric
phase.
Figure 6A shows line plots of the histograms for each
experiment and each gastric cell type. Despite some variability
between animals, spike densities peaked at roughly the same
phases between experiments. Figure 6B shows bar plots of the
mean bin values from all experiments (⫹SE). All five cell
types show different percentages of spikes in different phases
of the PD cycle (repeated-measures ANOVA, P ⬍ 0.0001 for
all measures). LG, MG, and GM firing peaked during the
interburst phase of the PD neurons, whereas DG and LPG
firing peaked during the PD neuron burst phase.
Phase relationships of the pyloric rhythm
ron bursts. During its bursts, Int1 was consistently hyperpolarized while the PD neuron was firing. During DG neuron bursts,
PD neuron bursts coincided with membrane potential depolarizations, and during LPG bursts, PD neuron bursts coincided
with the transition from depolarized to hyperpolarized membrane potentials. It should be noted that the conduction delay
between the STG and the pdn in H. americanus is only 30 –50
ms (Bucher et al. 2003, 2005), thus introducing an error of
maximally 5% into our measurements of relative timing between gastric neurons and PD neurons.
Pyloric modulation of gastric neurons is also evident in their
spike rates. We quantified this from extracellular recordings in
the following way: in 10 experiments, the pyloric cycle (between 2 consecutive PD burst starts) was divided into 20 bins,
and every gastric neuron spike was sorted into the corresponding bin. Then, every bin count was divided by the total number
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FIG. 7. Phase relationships in the pyloric rhythm (n ⫽ 17). Three cycles are
shown. Note that there appear to be 4 distinct phases: 1) PD, 2) IC, 3) LP, and
4) VD, PY, and AM. Bars indicating the AM neuron burst timing are shaded
in lighter gray because this neuron was bursting in only 7 of the 17 preparations. Error bars are SDs.
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FIG. 6. Pyloric modulation of gastric neuron spike rate. A: line plots of
histograms from 10 experiments. The pyloric phase was divided into 20 bins,
and gastric neuron spikes were sorted in to the corresponding bins. Bin values
were normalized to show percentage of counts per bin. The PD duty cycle
(⫹SD) is indicated on top. B: bar plots of histograms of the mean normalized
counts for all 10 experiments. Error bars are SEs. All measures show different
percentages of spikes in different phases of the PD cycle (repeated-measures
ANOVA, P ⬍ 0.0001 for all measures).
The phase relationships of the PD, LP, and PY neurons have
been described in detail before in H. americanus (Bucher et al.
2005; Thirumalai and Marder 2002) and H. gammarus (Meyrand et al. 2000), but the VD neuron and the IC neuron were not
previously included in any quantitative studies. Figure 7 shows
a bar chart of the pyloric phase relationships. For this analysis,
the latency between PD neuron burst starts and the burst starts
and ends of all pyloric neurons were measured and divided by
the cycle period (i.e., the time between 2 consecutive PD
neuron burst starts). Three cycles are shown. Except for the
AM neuron (see following text), only recordings were used in
which signals of all pyloric neurons were present (n ⫽ 17; AM:
n ⫽ 7).
The pyloric rhythm is usually described as a triphasic pattern
in which the bursts of the pacemaker group, the AB neuron and
the electrically coupled PD neurons, are followed by the LP
neuron and then the PY neurons. In C. borealis and P. interruptus, the VD neuron usually fires in the PY neuron phase,
and the IC neuron fires in the LP neuron phase (Mulloney
1987; Selverston and Miller 1980; Weimann et al. 1993). In H.
americanus, the IC neuron bursts between the PD neuron and
LP neuron phase, thereby making the pattern appear to have
four distinct phases (Fig. 7). Qualitatively, these phase relationships were consistent from animal to animal and not
obviously dependent on the cycle period. However, to show
statistically significant phase constancy between animals
would require a much larger sample, as shown in Bucher et al.
(2005), who used data from 99 animals.
The AM neuron was either silent or fired with the VD and
PY neurons, sometimes with only one spike per pyloric cycle.
We only included robustly bursting AM neurons in our anal-
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D. BUCHER, A. L. TAYLOR, AND E. MARDER
FIG. 8. Gastric modulation of pyloric
neuron membrane potential. Top 2 traces:
extracellular recordings of the LG, VD, and
IC neurons. The lower trace shows an intracellular recording of the IC neuron. The
pyloric-timed membrane potential oscillations change over the course of the gastric
cycle. Arrows indicate the 2nd part of a
biphasic depolarization that is strongest at
the start of the LG neuron burst and then
wanes within a few pyloric cycles. Dashed
lines indicate the change in the peaks and
troughs of the pyloric-timed oscillation,
which are both more depolarized at the time
of the start of the LG neuron burst and reach
minimum voltages around the middle of the
gastric cycle.
Gastric modulation of pyloric neurons
All pyloric neurons showed gastric modulation, albeit to
varying degrees. Figure 8 depicts a particularly prominent
example of such interactions. An intracellular recording from
the IC neuron and extracellular recordings of the IC neuron
(avn) and the VD and LG neurons (mvn) are shown. The
waveform of the IC neuron membrane potential oscillation, as
well as the IC neuron firing pattern, showed clear changes
during the gastric period. At the start of the gastric cycle (using
the LG neuron as the reference signal), the IC neuron showed
a double burst riding on top of a double depolarization that
waned over the next few cycles (arrows). In addition, both the
peaks and the troughs of the waveform oscillation were at
lower membrane potentials in the middle of the gastric cycle
(as indicated by broken lines).
We quantified the effect of gastric phase on the firing rate of
pyloric neurons (excluding AM) in 12 experiments, using
extracellular recordings. We divided the gastric phase (i.e., the
time between 2 consecutive LG neuron burst starts) into 10
bins and used the PD neuron burst starts to determine the
gastric phase bin in which a particular pyloric cycle took place.
We then measured the pyloric cycle period, the number of
spikes per burst, and the spike frequencies within bursts for the
PD, LP, PY, VD, and IC neurons. We also measured the
latency from PD neuron burst start to PD neuron burst end, and
the latencies from PD neuron burst starts to burst starts and
ends of the LP, PY, VD, and IC neurons. We calculated the
phase relationships of the pyloric rhythm by normalizing the
latencies to the pyloric cycle period. Figure 9 shows two
examples of these measures and their changes within the
gastric rhythm cycle for all 12 experiments. In addition, the
mean duty cycle of the LG neuron burst (⫹SD) is shown.
Figure 9A shows the pyloric cycle period and Fig. 9B shows
the latency of the PY neuron burst start (with respect to the PD
neuron burst start) as a function of the gastric phase. In both
cases, all experiments reveal larger values in the two bins
around the LG burst start. However, the magnitude of this
effect was variable across experiments. Two extreme cases are
shown in color for each measure.
Figure 10 shows the mean values of all measures from all
experiments. For clarity, SEs are not shown (except for the
pyloric cycle period). We tested all measures for significant
changes as a function of gastric phase (repeated-measurements
ANOVA). The significance level for each measure is indicated
by asterisks on the right of the plots. With the exception of the
latency of the PD neuron burst end, the phase of the PY neuron
burst end, and the PD spike frequency, all measures changed
significantly over the gastric cycle. The IC neuron generally
shows the largest gastric modulation. Many of the effects,
although statistically significant, are small. However, even
small changes in the firing pattern may be functionally relevant
at their readout, for example the contraction amplitude of
pyloric muscles (Morris et al. 2000; Thuma and Hooper 2002;
Thuma et al. 2003).
The influence of gastric phase on pyloric rhythm parameters
was not consistently strong or weak between different meaFIG. 9. Gastric modulation of the pyloric
rhythm. The gastric phase was divided into 10
bins, and PD neuron burst starts were used to
determine the gastric phase in which each pyloric cycle took place. A: change of the pyloric
cycle period as a function of the gastric phase
for 12 experiments. Note that even though peak
phases were consistent between experiments,
the magnitude of the pyloric cycle period
changes was variable. Two extreme cases are
shown in color. Gray bars indicate the mean
duty cycle of the LG neuron burst (⫹SD). B:
same type of plot as in A, here for the latency
of the PY neuron burst start (with respect to the
PD neuron burst start) as a function of the
gastric phase. Colored lines in A and B show
data from 4 different experiments.
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ysis. Intracellular recordings from silent AM neurons (not
shown) revealed clear pyloric modulation of the membrane
potential, peaking approximately with PY and VD activity.
SIMULTANEOUS FAST AND SLOW RHYTHMS IN STG NEURONS
3625
sures in the same experiment and also did not appear to be
correlated with how “strong” the gastric rhythm was. We found
no correlation with gastric cycle period, LG burst duration, LG
duty cycle, or number of LG spikes per burst (statistical
analysis not shown). However, it is possible that a much larger
sample size would be needed to establish such correlations.
Integer coupling between gastric and pyloric cycle periods
FIG. 10. Gastric modulation of the pyloric rhythm. Mean values from 12
experiments. ■, SE for the pyloric cycle period. For clarity, SEs for all other
measures are not shown. Significant changes as a function of the gastric cycle
are indicated by * on the left (repeated-measurements ANOVA; n.s.: not
significant; *, P ⬍ 0.05; **, P ⬍ 0.01; ***, P ⬍ 0.001). Actual P values: cycle
period, ⬍0.0001; latency; PD off: 0.2952; LP on, 0.0250; LP off, ⬍0.0001; PY
on, ⬍0.0001; PY off, ⬍0.0001; VD on, ⬍0.0001; VD off, ⬍0.0001; IC on,
⬍0.0001; IC off, ⬍0.0001; phase: PD off, ⬍0.0001; LP on, ⬍0.0001; LP off,
0.0350; PY on, 0.0466; PY off, 0.7726; VD on, 0.0432; VD off, ⬍0.0001; IC
on, ⬍0.0001; IC off, ⬍0.0001; #spikes/ burst: PD, 0.0290; LP, ⬍0.0001; PY,
0.0225; VD, 0.0084; IC, ⬍0.0001; spike frequency: PD, 0.3363; LP, ⬍0.0001;
PY, 0.0467; VD, ⬍0.0001; IC, 0.0085.
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In the preceding analyses, we investigated the dynamics of
the firing pattern of gastric neurons and pyloric neurons within
the reference frame of the other rhythm and showed that, to
some degree, the firing pattern of each STG neuron was
affected by the other rhythm. However, the magnitude of
effects found with these methods depends not only on the
strength of the interaction but also on the extent to which the
two rhythms are truly coordinated. Consequently, if the coordination between gastric and pyloric rhythms is not strict, it is
problematic to analyze one within the reference frame of the
other, because interactions can occur at different phases of the
reference cycle (Thuma and Hooper 2002). Therefore we
determined the extent to which the gastric cycle periods were
integer multiples of the pyloric cycle periods.
To that end, we counted the number of complete pyloric
cycles in every gastric cycle, i.e., between two consecutive LG
neuron burst starts. For the pyloric cycles occurring around the
start and the end of the gastric cycle, we calculated the
fractions of their periods that fell into the gastric cycle and
added it to the cycle count. This method is illustrated in Fig.
11A. Perfect integer multiple coupling would result in the
fraction of the pyloric cycle at the start of the gastric cycle and
the fraction at the end adding up to exactly 0 or exactly 1. In
contrast, no coupling would result in the sum of the fractions
taking any value between 0 and 2. Only experiments in which
ⱖ50 gastric cycles were recorded were used.
Figure 11B shows histograms from two preparations in
which every gastric cycle was scored for the number of pyloric
cycles that occurred within it. The pyloric cycle count values
were binned (bin size: 0.1), and each bin value was divided by
the total number of analyzed gastric cycles in that experiment.
Both show peaks around integer numbers in the respective
ranges. Figure 11C shows a histogram of the mean fraction of
counts of the number of pyloric cycles per gastric cycle for 20
preparations. It shows clear peaks at integer numbers of pyloric
cycles.
We also wanted to get a better sense of how consistent this
finding was across preparations. We therefore measured the
deviation from a given integer value for every gastric cycle in
every experiment. With this method, every data point could
take any value between ⫺0.5 and ⫹0.5, meaning that 0 would
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D. BUCHER, A. L. TAYLOR, AND E. MARDER
represent the integer (no matter what the actual integer value
for that gastric cycle was), and ⫺0.5 or ⫹0.5 would be the
maximum deviation from the integer. A histogram of the
integer deviation for each gastric cycle in a single preparation
is shown in Fig. 11D, along with a smoothed histogram (thick
black line). The smoothed histogram was calculated by adding
up Gaussian functions at the locations of each of the data
points. The SD of these Gaussian functions controlled the
degree of smoothing. The smoothed histogram shown in Fig.
11D appears to peak near zero deviation, suggesting the presence of integer-coupling.
However, it is possible for such a histogram to have a peak
near zero even if there is no true coupling between the two
rhythms. This can happen if by mere chance the mean cycle
period of one rhythm is an integer multiple of the cycle period
of the other, and the cycle-to-cycle variability is small. For
instance, consider two clocks. The minute hand of one clock
and the second hand of the other clock will appear to be
“integer-locked” to the extent they are both faithfully keeping
time. But this is not because there is any coupling between
them (as would be revealed if you broke one). But the minute
hand and the second hand of the same clock are integer-locked
because even if the cycle period of one varies, the other will
track with it.
To distinguish true integer coupling from “incidental” integer coupling, we used a “reshuffling” technique. For each
experiment, we first calculated the second moment (the average of the squares of all data points) of the integer deviation
data. This should be small for histograms that peak near zero
J Neurophysiol • VOL
and larger for ones that do not. We then randomly reshuffled
the sequence of pyloric periods to destroy any temporal relationship between the pyloric periods and the gastric period in
which they occur. If there was true integer coupling, we would
expect the integer deviation histogram to be less concentrated
around zero than in the true data. By generating many reshuffled data sets, we can approximate the distribution of second
moments for data that contain no true integer coupling. We can
then see how much of this reshuffled distribution was more
extreme than the value calculated from the data.
The mean of all smoothed histograms from 1,000 reshuffled
samples is shown in Fig. 11D, along with the mean SD (gray
and dashed curves). It is less concentrated around zero than the
smoothed histogram from the data, and the SDs suggest that it
is significantly so. Indeed we found that the second moment
was significantly different from the distribution of second
moments for reshuffled data, with P ⬍ 0.01. Overall, we found
that 17 of 20 preparations were significantly integer-coupled. A
smoothed histogram is shown for each preparation in Fig. 11E,
with significantly concentrated ones shown in black and not
significantly concentrated ones shown in gray.
Firing pattern of individual STG neurons reflects both the
pyloric and the gastric rhythm
In the preceding analysis, we found that coordination between the two rhythms, namely integer multiple coupling, was
present to varying degrees. Because this makes analyzing one
rhythmic pattern within the reference frame of the other prob-
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FIG. 11. Integer multiple coupling of pyloric and gastric cycle periods. A: recordings of mvn (VD and LG) and pdn (PD). Consecutive LG neuron burst starts were
used to define the gastric cycle (■). Pyloric cycles were counted from consecutive burst starts of the PD or VD neuron. The fractions of the pyloric cycles around the
start and the end of each gastric cycle were added to the number of complete pyloric cycles within the gastric cycle. B: overlaid histograms (bin size ⫽ 0.1) of the fraction
of the cycle count for 2 experiments. Both peak at integer values in their respected ranges. C: histogram of mean normalized cycle counts from 20 experiments. Again,
note the peaks at integer values. D: deviation from integer values. Histogram (bin size ⫽ 0.05) of the deviation from the nearest integer value of pyloric cycles for each
gastric cycle in 1 experiment. The black line represents a smoothed distribution generated from a sum of Gaussian functions, each centered on a data point. Values were
normalized by dividing by the number of gastric cycles. For comparison, a theoretical flat distribution of the data are shown (straight gray line). The sequence of pyloric
cycles was reshuffled to destroy any temporal relationship between the pyloric and gastric rhythms (see text). This was repeated 1,000 times and the deviation from
integer measured for each trial. The gray curve and dashed lines are the mean distribution from all trials ⫾ SD. The distribution was significantly less concentrated around
0 than the original data (P ⬍ 0.01). E: smoothed histograms from 20 experiments. In 17 experiments, the original data were significantly more concentrated around 0
than the distributions calculated from the reshuffled data.
SIMULTANEOUS FAST AND SLOW RHYTHMS IN STG NEURONS
forward and backward in time, was plotted as a histogram.
With appropriate bin sizes, such plots show peaks at time lags
that equal the period and multiples of that period of rhythmic
activity. In Fig. 12A, both the LG neuron and the DG neuron
show clear peaks at the gastric cycle period with very little, if
any, occurrence of smaller peaks corresponding to the pyloric
cycle period.
The VD neuron shows clear peaks corresponding to the
pyloric cycle period and its multiples. Those peaks have the
highest counts at time lags equal to the gastric period (open
arrows), as seen in the LG neuron and DG neuron autocorrelations. This is also true for the VD neuron in Fig. 12B,
indicating gastric modulation of the VD firing pattern.
In addition to peaks corresponding to the gastric cycle
period, the LG neuron and the DG neuron in Fig. 12B show
peaks corresponding to the pyloric cycle period. This is barely
detectable in the LG neuron but clearly visible in the DG
FIG. 12. Autocorrelations of STG neuron spike times.
A—C, left: 3 example recordings of the mvn (VD and LG) and
the dgn (DG). In C, no gastric rhythm was present, and the LG
neuron was silent. Right: autocorrelations. The interval between
every spike from a 20-min recording and every other spike in
the same trace is plotted as a histogram around 0 (bin size: 50
ms). The VD neuron shows peaks corresponding to the pyloric
cycle period (and its multiples) in all 3 examples. In A and B,
these peaks are highest at the interval corresponding to the
gastric cycle period (open arrows). The DG neuron shows
peaks corresponding to the gastric cycle period in A, peaks
corresponding to the gastric cycle period and multiples of the
pyloric cycle period ( ) in B, and only “pyloric peaks” in C. In
B, the LG neuron showed pyloric modulation in cycles in which
the duty cycle spanned ⬎1 pyloric cycle ( in left panel). This
pyloric modulation led to small shoulders at the peaks in the
autocorrelation that correspond to the gastric cycle period
(arrowheads in right panel).
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lematic, we also analyzed the firing pattern of each individual
neuron solely based on its spike times.
Figure 12 shows extracellular recordings of the VD, LG, and
DG neurons in three different experiments. Figure 12A shows
an example in which both the DG and the LG neuron fired
strong bursts with many spikes and little apparent modulation
in pyloric time. Figure 12B shows an example with weaker
firing but strong pyloric modulation of the DG firing pattern.
Figure 12C shows an example in which no gastric rhythm was
present, the LG neuron was silent, and the DG neuron fired
only in pyloric time. In all three examples, the VD neuron
showed no apparent modulation of its firing pattern in gastric
time.
As a first pass, we used autocorrelation histograms of the
spike times to visualize the presence of pyloric and gastric
contributions to the firing pattern (Fig. 12, right). The time lag
from every spike to every other spike in the same trace, both
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D. BUCHER, A. L. TAYLOR, AND E. MARDER
neuron (open arrows). The LG neuron in this recording had a
relatively small duty cycle that did not span multiple pyloric
cycles in every gastric cycle. However, when it did, its firing
pattern was clearly modulated in pyloric time (arrowheads in
the mvn recording), which presumably results in the small
shoulder of the gastric peak in the autocorrelation (arrowheads). The autocorrelations of the VD neuron and the DG
neuron in Fig. 12C only show peaks corresponding to the
pyloric cycle period.
Quantification of pyloric and gastric contribution to STG
neuron firing patterns
FIG. 13. Spectral analysis of STG neuron spike activity. A–C: plots of
spectral density vs. frequency for the VD, LG, and DG neuron recordings
shown in Fig. 12B. The pyloric (red) and gastric (green) cycle frequencies are
indicated by arrows. Shaded areas correspond to the frequency ranges used in
the calculation of gastric and pyloric root-mean-square (RMS) amplitude
ratios. D: gastric and pyloric RMS amplitude ratios for all STG neuron types
(n ⫽ 10, AM: n ⫽ 5).
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On the qualitative level, the autocorrelations showed that the
firing pattern of every STG neuron type can simultaneously
contain timing information about both the fast pyloric rhythm
and the slower gastric rhythm. However, we also wanted to
establish the degree to which each rhythm contributes to the
firing pattern of each individual neuron type.
To quantify the contribution of each rhythm to each cell’s
firing pattern, we examined the power spectrum of each cell’s
spike train (Fig. 13, A–C). We found that the spectra had most
of their power in a series of sharp peaks, the first at the gastric
mill frequency, and the others at integer multiples of this
frequency. This is expected because any nonsinusoidal periodic signal with a given frequency can be written as a sum of
sinusoids, the first at the given frequency, and the rest at integer
multiples of the given frequency (Siebert 1986). The given
frequency is often called the “fundamental,” and the other
sinusoids are called “harmonics” of this fundamental. A purely
gastric cell would be expected to have peaks at the gastric
frequency (the fundamental) and integer multiples (harmonics)
of the gastric frequency, and a purely pyloric cell would be
expected to have peaks at the pyloric frequency and integer
multiples of the pyloric frequency. Pyloric cells (VD in Fig.
13A) showed large peaks at the pyloric cycle frequency (red
arrow) and integer multiples of it with the height of these
pyloric-harmonic peaks decreasing steadily with increasing
frequency. In addition, most pyloric cells also showed small
peaks at the gastric frequency (green arrow), reflecting the
pervasive gastric influences in the system. For gastric cells that
had little or no apparent pyloric modulation of their firing
pattern (LG in Fig. 13B), most of the power in the spectra were
in peaks at the gastric frequency and harmonics of it, and the
height of the harmonic peaks decreased steadily with increasing frequency. In cells that showed strong contributions of both
rhythms (DG in Fig. 13C), we observed a blending of the
purely pyloric and purely gastric spectra. In these cells, the
height of the gastric harmonics did not decrease steadily with
increasing frequency. Because of integer-locking of the gastric
and pyloric frequencies, the pyloric frequency was a harmonic
of the gastric frequency, and the peak at the pyloric fundamental tended to be much larger than it would have been in a purely
gastric cell. The gastric harmonics just above and just below
SIMULTANEOUS FAST AND SLOW RHYTHMS IN STG NEURONS
Firing pattern modulation by other rhythms
In five experiments, we recorded the esophageal rhythm,
which is generated in the OG and CoGs and typically has a
period somewhere in between the pyloric period and the gastric
period (9.02 ⫾ 2.43). We never observed clear firing pattern
modulation of any of the pyloric and gastric neurons in time
with that rhythm.
The cardiac sac rhythm, which has a cycle period on the
order of tens of seconds to several minutes in the spiny lobster,
has been shown to strongly influence pyloric firing patterns
(Ayali and Harris-Warrick 1998; Moulins and Vedel 1977;
Thuma and Hooper 2003). However, Meyrand et al. (1994)
never saw spontaneous cardiac sac rhythms in H. gammarus. In
one experiment, the gastric activity showed modulation with a
period of tens of seconds, but we did not have a reference
signal to determine if this was cardiac sac activity.
DISCUSSION
The simultaneous expression of more than one temporal
pattern by neurons and networks is a widespread phenomenon.
In the mammalian forebrain, oscillations are present in different frequency bands (Buzsaki and Chrobak 1995; Buzsaki and
Draguhn 2004), and single neurons may express more than one
type of oscillation at the same time (Steriade 2005; Steriade et
al. 1993). In sensory systems, different firing modes can
encode parallel and complementary information transfer (Oswald et al. 2004). In motor systems, interactions and coordination are particularly important, because many behaviors
involve more than one body part (Chrachri and Neil 1993;
Larson et al. 1994; Lieske et al. 2000; Morin and Viala 2002;
Potts et al. 2005), and the coordinated execution of movements
in neighboring body parts is important to avoid mechanical
interference.
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Quantification of circuit interactions
Although it may be commonplace for neurons to be driven
by two or more rhythmic inputs, or even to be part of multiple
rhythm-generating networks (Weimann and Marder 1994),
quantification of the extent to which a neuron’s firing reflects
each of the rhythms is not easy, and one of our goals was to
attempt this task using the pattern generating networks of the
stomatogastric nervous system. We analyzed the interactions
between the pyloric and the gastric rhythm in the lobster, H.
americanus. Weimann et al. (1991) scored the STG neurons in
C. borealis for the relative time they participate in either the
gastric or the pyloric rhythm. This was relatively straightforward in a situation where neurons switch from one rhythm to
the other (particularly when one of the rhythms is not always
active) and when pyloric modulation during gastric bursts and
gastric modulation of burst parameters in pyloric neurons is
ignored. However, a quantification of the influence of one
pattern on the activity of neurons that predominantly are
critically involved in producing another pattern requires a
different approach.
We analyzed the interactions between gastric and pyloric
rhythms under different premises. A CPG can be viewed as a
circuit, the constituent neurons of which produce a certain type
of activity and are coordinated in a specific way. In the case of
interactions with another circuit, the activity and the intracircuit coordination may change within the reference frame of
the other circuit’s activity. We show here that the firing pattern
produced by gastric neurons is influenced by the much faster
pyloric rhythm. Some gastric neurons show pyloric-timed
interruptions of their gastric-timed bursts, others show trailing
firing in pyloric time between stronger gastric-timed bursts.
We also show that the activity of the pyloric neurons, and their
coordination within the pyloric pattern, change within the
reference frame of the gastric cycle.
The presence of inter-circuit interactions is a separate issue
from true coordination between the two patterns. In fact,
spontaneous gastric and pyloric rhythms show no integer
coupling in P. interruptus (Thuma and Hooper 2002). Nevertheless the overall spike frequency of pyloric neurons is
strongly influenced by the gastric pattern. Thuma and Hooper
(2002) show that using the gastric cycle as the frame of
reference for a quantitative analysis in the absence of coordination leads to an underestimation of the magnitude of the
interaction. This happens because of averaging between many
gastric cycles in which pyloric cycles can occur at different
times.
In H. americanus, the coordination between the two rhythms
is stronger, as seen from the presence of integer coupling of the
pyloric and gastric cycle periods. However, this coupling is
variable, and 3 of 20 preparations failed to express it significantly. In addition, we show that all STG neurons express both
patterns to some degree. Therefore there is no pure version of
either of the two patterns that can serve as the reference frame
for analyzing modulation of the other circuit.
In light of the preceding data, we also analyzed the spike
patterns of each type of STG neuron independently. The goal
was to quantify the contributions of each rhythm to the firing
pattern. Integrating frequency bands of the power spectra that
correspond to the cycle frequencies of the two rhythms provides a method that is independent of the presence of intercir-
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the pyloric fundamental also tended to be enhanced. Above the
pyloric fundamental, furthermore, the gastric harmonics that
were not also pyloric harmonics tended to be very small or
absent.
Based on these considerations, we felt justified in declaring
all power below a particular cutoff (typically ⬃0.3 Hz) to be
gastric and all power in sharp peaks at the pyloric cycle
frequency and multiples thereof to be pyloric. We quantified
the gastric and pyloric contribution to the firing pattern of each
neuron by integrating the power in the respective bands (red
and green shading in Fig. 13, A–C) and then converting each to
a root-mean-square (RMS) amplitude by taking the square
root. These values were then normalized by dividing by the
RMS amplitude in a wide band from 0 to 6 Hz. Although the
gastric/pyloric ranges may not capture all of the gastric/pyloric
power (e.g., Fig. 13B), they capture enough of it to be a useful
quantification of the extent to which a cell’s activity reflects
gastric or pyloric activity.
Figure 13D shows the RMS amplitude ratios for the pyloric
and gastric frequency ranges for every neuron type from 10
experiments. The AM neuron was only active in five of these
experiments. Among the pyloric neurons, the gastric rhythm
had the largest contribution to the firing pattern of the IC
neuron. Among the gastric neurons, the pyloric rhythm had the
largest contribution to the firing pattern of the DG neuron and
the LPG neurons.
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Is there a common baseline state of the isolated STNS from
preparation to preparation?
Under the influence of different neuromodulators and as a
result of differential activation of descending modulatory neurons, the phase relationships of both the gastric pattern and the
pyloric pattern can be very different (Dickinson and Nagy
1983; Eisen and Marder 1984; Flamm and Harris-Warrick
1986a,b; Heinzel 1988b; Heinzel and Selverston 1988; Marder
and Hooper 1985; Marder and Weimann 1992; Marder et al.
2005; Meyrand et al. 2000; Nagy and Dickinson 1983; Norris
et al. 1994; Nusbaum and Beenhakker 2002; Nusbaum et al.
2001). Nevertheless, the isolated STNS appears to have a
comparable baseline activation state from preparation to preparation. In H. americanus, the pyloric cycle period can vary
between 1.1 and 2.6 s from preparation to preparation, but the
phase relationships are well conserved (Bucher et al. 2005).
Here we also found that the gastric rhythm was fairly
consistent from preparation to preparation. To some degree,
what constitutes a small or a large amount of variability lies in
the eye of the beholder. Nonetheless, within the variability seen
in every parameter we analyzed, we found gradual differences
instead of distinct types of gastric activity or gastro-pyloric
interactions. Distinct types of gastric activity or gastro-pyloric
interactions are found in C. borealis when different modulatory
projection neurons and/or sensory neurons are independently
stimulated (Blitz et al. 2004; Norris et al. 1994; Nusbaum et al.
2001), but it is not known how consistent spontaneous activity
of different modulatory projection neurons is.
In our data, the most extreme disparity appears to exist
between the preparations that did not express spontaneous
gastric activity and those that did. However, in the absence of
gastric activity, the pyloric rhythm was slower (Fig. 3). Therefore it is possible that there is a continuum of how much overall
descending modulatory activation of the two rhythms is present
and that the threshold for activation of the gastric rhythm is
higher than the one for the pyloric rhythm. This is not to say
that modulatory input should be viewed as a general “arousal”
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signal. It is now well established that activation and modulation of STG circuits is achieved through the activity of specific
modulatory neurons and specific modulatory substances with
specific cellular and synaptic targets (Blitz et al. 1995; Dickinson and Nagy 1983; Eisen and Marder 1984; Harris-Warrick
et al. 1998; Nagy and Dickinson 1983; Nusbaum and Beenhakker 2002; Swensen and Marder 2000), and many modulatory neurons have target neurons in both the pyloric and gastric
circuits (Blitz et al. 1999; Christie et al. 2004; Claiborne and
Selverston 1984; Dickinson and Nagy 1983; Meyrand et al.
1991, 1994; Nagy et al. 1988; Nusbaum et al. 1992; Swensen
and Marder 2000; Swensen et al. 2000). Nevertheless, only the
pyloric rhythm sometimes persists even in the absence of
modulatory inputs (Luther et al. 2003; Russell 1976; Weimann
et al. 1997), and bath application of neuromodulators activates
the gastric rhythm less readily than the pyloric rhythm (Heinzel
and Selverston 1988; Marder et al. 1986).
Functional implications of network interactions
What do the interactions between gastric and pyloric activity
mean with respect to the actual motor output? The ultimate
decision about which part of the information present in a signal
is functionally relevant is made at the readout, i.e., the postsynaptic site. For example, different types of synaptic dynamics
can differentially filter frequency components of a presynaptic
signal (Bertram 2001).
Accordingly, how much of the gastric and pyloric contributions to the firing pattern of a STG neuron is functionally
relevant is decided at the structures postsynaptic to it. In P.
interruptus, the overall spike frequency of pyloric neurons is
modulated both through interactions with the gastric and the
cardiac sac rhythms (Thuma and Hooper 2002, 2003). These
changes, although subtle when considering predominant frequencies in the activity, can have large effects on the contraction amplitude of pyloric muscles (Morris et al. 2000; Thuma
et al. 2003). This is a consequence of slow contraction and
relaxation properties of the muscles that lead to low-pass
filtering of the input (Hooper and Weaver 2000; Morris and
Hooper 1998; Morris et al. 2000).
The contraction properties of stomach muscles in H. americanus have not been studied in detail. However, the gastric
modulation of pyloric neuron firing may have similar effects on
pyloric muscle contractions as in P. interruptus. Relatively
slow relaxation time constants may lead to substantial amplitude changes over the gastric cycle. Possible effects of pyloric
modulation of gastric neuron firing on gastric mill muscles are
equally dependent on contraction properties. With very slow
contraction/relaxation time constants, pyloric modulation of
neurons innervating gastric mill muscles may result in little or
no pyloric-timed contractions. With faster time constants, gastric mill muscles could contract in pyloric time on top of their
gastric contractions or even produce “pure” pyloric contractions but confined to a specific phase of the gastric cycle.
Endoscopic imaging of the gastric mill in intact crabs has
shown that the lateral teeth actually move in both gastric and
pyloric time (Heinzel et al. 1993). It is also interesting to note
that the contraction/relaxation time constants of gastric mill
muscles in the crab can be changed substantially under the
influence of different neurohormones (Jorge-Rivera et al.
1998). In principle, this means that the amount of pyloric-timed
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cuit coordination. It also provides a means to collapse the
influence of a pattern on the spiking activity of a given neuron
into a single number, which is helpful for doing preparationto-preparation comparisons and will be even more necessary
for future quantifications of the extent to which neuromodulatory influences alter the interaction between the pyloric and
gastric networks.
However, some caution is advisable when interpreting these
numbers. For example, a neuron that fires in pyloric time, but
only during a particular phase of the gastric cycle, will be
“more pyloric” the longer its duty cycle in the gastric cycle
according to our measure. Nevertheless the spectral analysis
yielded results generally similar to what we found when we
analyzed the pyloric firing patterns within the reference frame
of the gastric rhythm, and the gastric firing pattern within the
reference frame of the pyloric rhythm. Among the pyloric
neurons, the gastric rhythm had the largest contribution to the
firing pattern of the IC neuron. Among the gastric neurons, the
pyloric rhythm had the largest contribution to the firing pattern
of the DG neuron and the LPG neurons. The magnitude and
functional relevance of these effects ultimately have to be seen
in the context of the actual motor output (see following text).
SIMULTANEOUS FAST AND SLOW RHYTHMS IN STG NEURONS
contraction can be changed even if the pyloric contribution to
the neuronal firing pattern stays the same.
Because the STG motor neurons are also part of the networks that generate the pyloric and gastric rhythms, they also
have targets within the STG itself. As the synaptic connections
within the STG show frequency-dependent synaptic depression
(Manor et al. 1997; Nadim et al. 1999), and the membrane
properties of STG neurons themselves may have slow dynamics (Goaillard and Marder 2005; Hooper 1998; Pulver et al.
2005), the extent to which the simultaneous expression of
pyloric and gastric activity shapes the dynamics of circuit
operation is at present hard to determine. It will be interesting
in other systems that express two or more patterns simultaneously to determine the extent to which this is “seen” by their
network targets.
We thank C. Johnson for providing some of the data.
GRANTS
This work was supported by National Institute of Neurological Disorders
and Stroke Grants NS-17813 to E. Marder and NS-050928 to A. L. Taylor.
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